Horn tooting coming here – but since I invested the time to actually generate the numbers, perhaps people might be interested in them ☺
In the limit of long enough time, the temperature distribution of Andersen is indeed the canonical distribution. And that length of time required to get a correct ensemble is not that long at all – a few hundred randomizations per particle seems to do it. It actually works quite well pratically, as well as any other algorithm. See: http://pubs.acs.org/doi/abs/10.1021/ct300688p, especially table 2, for a comparison of different themostats and how well they match the canonical distribution an comparison to other thermostats.
In a related note, I’ll plug my paper here on transport effects of different thermostats: http://pubs.acs.org/doi/abs/10.1021/ct400109a. All thermostats fail to give truly physical dynamics for one reason or another. For Langevin, there are no magical particles applying friction uniformly everywhere, for Nose-Hoover, there’s no physical mechanism for isotropically adding or subtracting thermal energy everywhere, for Andersen, random collisions don’t come from nowhere, etc. The failure modes can generally be seen outline in the paper, although these are mostly properties that depend on the short-time correlation in velocities – rare events could have different properties. Turns out Berendsen, although really crappy at giving an NVT ensemble, gives decent diffusion constants if the time constant is not too short (as do several others – but not Andersen or Langevin, at least for short time constants). My personal choice for closest thermostat to physics would be Langevin on the solvent, but not on the system of interest (assuming something like a protein is the system of interest isn’t actually the solvent). We play around a little with that in the paper, and are certainly not the first to suggest it. Anyway, read the paper for more details. Happy to talk more about the results there.
Best,
~~~~~~~~~~~~~~~~
Michael Shirts
Associate Professor
michael.shirts.colorado.edu
http://www.colorado.edu/lab/shirtsgroup/
Phone: (303) 735-7860
Office: JSCBB C123
Department of Chemical and Biological Engineering
University of Colorado Boulder
On 4/1/17, 5:05 PM, "Adrian Roitberg" <roitberg.ufl.edu> wrote:
Well, I stand semi-corrected.
From a purely mathematical point of view, Andersen indeed keeps the
correct NVT ensemble. It is basically a series of microcanonical
ensembles, which every time you apply the thermostat, switch total E
(and total momentum) in a markov-chain way and hence build a canonical
ensemble eventually.
In real life, extracting random forces and velocities according to a
Boltzmann distribution, which is what the proof of the correct NVT
ensemble requires, is not an easy thing to do for a finite system
running for a finite amount of time.
Also to keep in mind, Andersen destroys time continuity so diffusion
quantities are not correct. Also, reassigning momenta makes the system
memory very short, so barrier crossing rates can go down.
Adrian
On 4/1/17 2:21 PM, Jason Swails wrote:
> I thought it did...
>
> --
> Jason M. Swails
>
>> On Apr 1, 2017, at 5:02 PM, Adrian Roitberg <roitberg.ufl.edu> wrote:
>>
>> Hi
>>
>> Technically, no, Andersen does not give you a true canonical ensemble.
>> However, you would have to look VERY closely at a simulation to figure
>> out that it is not.
>>
>> adrian
>>
>>
>>> On 4/1/17 12:04 PM, pengfei li wrote:
>>> Hi everyone,
>>>
>>> A quick question, will ntt=2 (the Andersen temperature coupling scheme) give a canonical ensemble? Thanks!
>>>
>>> Best regards,
>>> Pengfei
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>> --
>> Dr. Adrian E. Roitberg
>> University of Florida Research Foundation Professor.
>> Department of Chemistry
>> University of Florida
>> roitberg.ufl.edu
>> 352-392-6972
>>
>>
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--
Dr. Adrian E. Roitberg
University of Florida Research Foundation Professor.
Department of Chemistry
University of Florida
roitberg.ufl.edu
352-392-6972
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Received on Sat Apr 01 2017 - 19:30:02 PDT
